Solve for $x$ and $y$ by deriving an expression for $y$ from the second equation, and substituting it back into the first equation. $\begin{align*}-3x+2y &= 2 \\ -6x-2y &= -5\end{align*}$
Solution: Begin by moving the $x$ -term in the second equation to the right side of the equation. $-2y = 6x-5$ Divide both sides by $-2$ to isolate $y$ $y = {-3x + \dfrac{5}{2}}$ Substitute this expression for $y$ in the first equation. $-3x+2({-3x + \dfrac{5}{2}}) = 2$ $-3x - 6x + 5 = 2$ Simplify by combining terms, then solve for $x$ $-9x + 5 = 2$ $-9x = -3$ $x = \dfrac{1}{3}$ Substitute $\dfrac{1}{3}$ for $x$ back into the top equation. $-3( \dfrac{1}{3})+2y = 2$ $-1+2y = 2$ $2y = 3$ $y = \dfrac{3}{2}$ The solution is $\enspace x = \dfrac{1}{3}, \enspace y = \dfrac{3}{2}$.